Some Results on $s^{n-k}$ Fractional Factorial Designs with Minimum Aberration or Optimal Moments

Some lower bounds of centered $$L_2$$ L 2 -discrepancy of $$2^{s-k}$$ 2 s - k designs and their complementary designs

“…When k = 1, it is well known that the MA 2 s−1 design is also a uniform design with defining relation I = 12 · · · s. For the case k ≤ 4, Chen and Wu (1991) provided some results on 2 s−k designs with minimum aberration and their construction. Fang and Mukerjee (2000) indicated that 2 s−k designs with minimum aberration behave well in term of uniformity in the sense of keeping CD(F) small.…”

“…Fang and Mukerjee (2000) indicated that 2 s−k designs with minimum aberration behave well in term of uniformity in the sense of keeping CD(F) small. Therefore, one can construct 2 s−k designs with small centered L 2 -discrepancy among all regular designs with the same parameters via the method of Chen and Wu (1991) for k ≤ 4. For k ≥ 5, the construction of 2 s−k designs with minimum aberration is more complicated and the work has to be done by combining some computer research methods, as pointed in Chen and Wu (1991).…”

“…Therefore, one can construct 2 s−k designs with small centered L 2 -discrepancy among all regular designs with the same parameters via the method of Chen and Wu (1991) for k ≤ 4. For k ≥ 5, the construction of 2 s−k designs with minimum aberration is more complicated and the work has to be done by combining some computer research methods, as pointed in Chen and Wu (1991). Now we use two examples to show our results.…”

Optimal Blocking Schemes for 2nand 2n—pDesigns

“…The mathematical equivalence to the MA criterion for FF designs enables us to obtain theoretical results on MA blocking schemes by drawing on the similar results on MA 2"-P designs (e.g., Chen and Wu 1991;Chen 1992;Tang and Wu in press) and to construct MA blocking schemes by using the same algorithm described by Chen, Sun, and Wu (1993) (henceforth abbreviated as CSW) for the 2+P FF designs. There is, however, a major difference between the two problems.…”

Fractional Resolution and Minimum Aberration in Blocked 2n—kDesigns

“…Typically, there are many choices of how to assign factors to columns with varying impact on this inability to separate effects. A commonly used criterion for ranking designs on this aspect is resolution and its refinement, minimum aberration (MA) (Box and Hunter 1961;Fries and Hunter 1980;Franklin 1984;Chen and Wu 1991;Chen, Sun, and Wu 1993).…”